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A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in ${\mathbb C}^n$ are introduced. Basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. Furthermore, it is shown that if the Schwarzian derivative of a pluriharmonic mapping vanishes then the analytic part of this mapping is a M\"obius transformation. Some observations are made related to the dilatation of pluriharmonic mappings and to the dilatation of their affine transformations, revealing differences between the theories in the plane and in higher dimensions. An example is given that rules out the possibility for a shear construction theorem to hold in ${\mathbb C}^n$, for $n\geq2$., Comment: 24 pages; to appear in Journal of Mathematical Analysis and Applications

The current availability of soil moisture data over large areas comes from satellite remote sensing technologies (i.e., radar-based systems), but these data have coarse resolution and often exhibit large spatial information gaps. Where data are too coarse or sparse for a given need (e.g., precision agriculture), one can leverage machine-learning techniques coupled with other sources of environmental information (e.g., topography) to generate gap-free information and at a finer spatial resolution (i.e., increased granularity). To this end, we develop a spatial inference engine consisting of modular stages for processing spatial environmental data, generating predictions with machine-learning techniques, and analyzing these predictions. We demonstrate the functionality of this approach and the effects of data processing choices via multiple prediction maps over a United States ecological region with a highly diverse soil moisture profile (i.e., the Middle Atlantic Coastal Plains). The relevance of our work derives from a pressing need to improve the spatial representation of soil moisture for applications in environmental sciences (e.g., ecological niche modeling, carbon monitoring systems, and other Earth system models) and precision agriculture (e.g., optimizing irrigation practices and other land management decisions)., Comment: 10 pages, 11 figures, 1 table

We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming that the small system is of finite type), we prove that both effective dynamics capture the long-term behaviour of the system: existence of a unique asymptotic state for them implies the same property for the respective exact dynamics--provided that the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case in which the small system and the chain element are spins., Comment: Final version accepted in J. Stat. Phys., some proofs corrected. 18 pages, no figures

This paper describes the formation of, and initial results for, a new FLUXNET coordination network for ecosystem-scale methane (CH4) measurements at 60 sites globally, organized by the Global Carbon Project in partnership with other initiatives and regional flux tower networks. The objectives of the effort are presented along with an overview of the coverage of eddy covariance (EC) CH4 flux measurements globally, initial results comparing CH4 fluxes across the sites, and future research directions and needs. Annual estimates of net CH4 fluxes across sites ranged from −0.2 ± 0.02 g C m(exp -2) yr(exp -1) for an upland forest site to 114.9 ± 13.4 g C m(exp -2) yr(exp -1) for an estuarine freshwater marsh, with fluxes exceeding 40 g C m(exp -2) yr(exp -1) at multiple sites. Average annual soil and air temperatures were found to be the strongest predictor of annual CH4 flux across wetland sites globally. Water table position was positively correlated with annual CH4 emissions, although only for wetland sites that were not consistently inundated throughout the year. The ratio of annual CH4 fluxes to ecosystem respiration increased significantly with mean site temperature. Uncertainties in annual CH4 estimates due to gap-filling and random errors were on average ±1.6 g C m(exp -2) yr(exp -1) at 95% confidence, with the relative error decreasing exponentially with increasing flux magnitude across sites. Through the analysis and synthesis of a growing EC CH4 flux database, the controls on ecosystem CH4 fluxes can be better understood, used to inform and validate Earth system models, and reconcile differences between land surface model- and atmospheric-based estimates of CH4 emissions.

Incorporating ecological disturbance into biogeochemical models is critical for estimating current and future carbon stocks and fluxes. In particular, anthropogenic disturbances, such as forest conversion and wood harvest, strongly affect forest carbon dynamics within North America. This paper summarizes recent (2000.2008) rates of extraction, including both conversion and harvest, derived from national forest inventories for North America (the United States, Canada, and Mexico). During the 2000s, 6.1 million ha/yr were affected by harvest, another 1.0 million ha/yr were converted to other land uses through gross deforestation, and 0.4 million ha/yr were degraded. Thus about 1.0% of North America fs forests experienced some form of anthropogenic disturbance each year. However, due to harvest recovery, afforestation, and reforestation, the total forest area on the continent has been roughly stable during the decade. On average, about 110 m3 of roundwood volume was extracted per hectare harvested across the continent. Patterns of extraction vary among the three countries, with U.S. and Canadian activity dominated by partial and clear ]cut harvest, respectively, and activity in Mexico dominated by conversion (deforestation) for agriculture. Temporal trends in harvest and clearing may be affected by economic variables, technology, and forest policy decisions. While overall rates of extraction appear fairly stable in all three countries since the 1980s, harvest within the United States has shifted toward the southern United States and away from the Pacific Northwest.